On the fractal properties of cosmic rays and Sun dynamics cross-correlations

We investigate the cosmic rays and ten physical parameters of heliosphere behavior considering the scaling features of their temporal evolution. Our analysis start with the cosmic rays measurements by a neutron monitor station located in Moscow, as well sunspot, Ap index, Na/Np, Alfven mach number, DST index, Kp index, Plasma beta ( β ), Proton temperature, F_10.7 index and Field magnitude |B| (Interplanetary Magnetic Field, IMF), for the period 1976 to early 2020. Each of these datasets was analyzed by using the Multifractal Detrended Fluctuation Analysis and Multifractal Detrended Cross-Correlation Analysis in order to investigate intrinsic properties, like self-similarity and the spectrum of singularities. The main result obtained is that the cosmic rays time series as well the 10 heliospheric parameters exhibit positive long-range correlations with multifractal behavior.